Is it possible to make a displace modifier collide with other objects? if not, is there a way to make the food not go through the cooking pot?
See Vertex Groups.  There are plenty of postings here at BSE to be searched.
By selecting the top of the delicious tuna fish casserole in Edit Mode and making it into  a vertex group named say &quot;TCTOP&quot; you can displace only exactly the top of mesh.